Problem: $-7tu + 10tv - 10t + 3 = -9u + 6$ Solve for $t$.
Answer: Combine constant terms on the right. $-7tu + 10tv - 10t + {3} = -9u + {6}$ $-7tu + 10tv - 10t = -9u + {3}$ Notice that all the terms on the left-hand side of the equation have $t$ in them. $-7{t}u + 10{t}v - 10{t} = -9u + 3$ Factor out the $t$ ${t} \cdot \left( -7u + 10v - 10 \right) = -9u + 3$ Isolate the $t$ $t \cdot \left( -{7u + 10v - 10} \right) = -9u + 3$ $t = \dfrac{ -9u + 3 }{ -{7u + 10v - 10} }$ We can simplify this by multiplying the top and bottom by $-1$. $t= \dfrac{9u - 3}{7u - 10v + 10}$